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One of the zeros of the given quadratic function is x=-5.5.
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: [tex]D=b^2-4ac[/tex] . And after that you should apply the discriminant in the formula: [tex]x=\frac{-b\pm \sqrt{D} }{2a}[/tex]
In this equation:
a=4
b=24
c=11
[tex]D=b^2-4ac=24^2-4\cdot \:4\cdot \:11}=576-176=400[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{D} }{2a}\\ \\ x_{1,\:2}=\frac{-24\pm \sqrt{24^2-4\cdot \:4\cdot \:11}}{2\cdot \:4}\\ \\ x_{1,\:2}=\frac{-24\pm \sqrt{400}}{8}\\ \\ x_{1,\:2}=\frac{-24\pm 20}{8}[/tex]
Then,
[tex]x_1=\frac{-24+20}{2\cdot \:4}\\ \\ x_1=\frac{-4}{8}=\frac{-1}{2}=-0.5[/tex]
and
[tex]x_2=\frac{-24-20}{2\cdot \:4}\\ \\ x_1=\frac{-44}{8}=\frac{-11}{2}=-5.5[/tex]
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